Classical Physical Geodesy

Living reference work entry

Abstract

Geodesy can be defined as the science of the figure of the Earth and its gravitational field, as well as their determination. Even though today the figure of the Earth, understood as the visible Earth’s surface, can be determined purely geometrically by satellites, using Global Positioning System (GPS) for the continents and satellite altimetry for the oceans, it would be pretty useless without gravity. One could not even stand upright or walk without being “told” by gravity where the upright direction is. So as soon as one likes to work with the Earth’s surface, one does need the gravitational field. (Not to speak of the fact that, without this gravitational field, no satellites could orbit around the Earth.)

Keywords

Global Position System Harmonic Function Centrifugal Force Analytical Continuation Geoidal Height 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author thanks his colleagues in the Institute of Navigation and Satellite Geodesy at TU Graz for constant support and help in the wonderful atmosphere in the institute, especially to B. Hofmann-Wellenhof, S. Berghold, F. Heuberger, N. Kühtreiber, R. Mayrhofer, and R. Pail, who has carefully read the manuscript.

References

Monographs

  1. Bruns H (1878) Die Figur der Erde. Publikation des Preussischen Geodätischen Instituts, BerlinGoogle Scholar
  2. Courant R, Hilbert D (1962) Methods of mathematical physics, vol 2. Wiley-Interscience, New YorkMATHGoogle Scholar
  3. Fock V (1959) The theory of space-time and gravitation. Pergamon, LondonMATHGoogle Scholar
  4. Frank P, von Mises R (eds) (1930) Die Differential- und Integralgleichungen der Mechanik und Physik, 2nd edn, Part 1: Mathematischer Teil. Vieweg, Braunschweig (reprint 1961 by Dover, New York and Vieweg, Braunschweig)Google Scholar
  5. Helmert FR (1884) Die mathematischen und physikalischen Theorien der Höheren Geodäsie, Part 2. Teubner, Leipzig (reprint 1962)Google Scholar
  6. Hofmann-Wellenhof B, Moritz H (2005) Physical geodesy. Springer, WienGoogle Scholar
  7. Hofmann-Wellenhof B, Legat K, Wieser M (2003) Navigation-principles of positioning and guidance. Springer, WienGoogle Scholar
  8. Hotine M (1969) Mathematical geodesy. ESSA Monograph, vol 2. U.S. Department of Commerce, Washington, DC (reprint 1992 by Springer)Google Scholar
  9. Kellogg OD (1929) Foundations of potential theory. Springer, Berlin (reprint 1954 by Dover, New York, and 1967 by Springer)Google Scholar
  10. Krarup T (1969) A contribution to the mathematical foundation of physical geodesy, vol 44. Danish Geodetic Institute, Copenhagen (reprinted in (Borre 2006))Google Scholar
  11. Lorenz E (1993) The essence of chaos. University of Washington, SeattleCrossRefMATHGoogle Scholar
  12. Marussi A (1985) Intrinsic geodesy. Springer, BerlinCrossRefGoogle Scholar
  13. Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. Freemann, San FranciscoGoogle Scholar
  14. Moritz H (1967) Kinematical geodesy. Report 92. Department of Geodetic Science, Ohio State University, ColumbusGoogle Scholar
  15. Moritz H (1980) Advanced physical geodesy. Wichmann, KarlsruheGoogle Scholar
  16. Moritz H, Hofmann-Wellenhof B (1993) Geometry, relativity, geodesy. Wichmann, KarlsruheGoogle Scholar
  17. Moritz H, Mueller II (1987) Earth rotation-theory and observation. Ungar, New YorkGoogle Scholar
  18. Neumann F (1887) In: Neumann C (ed) Vorlesungen über die Theorie des Potentials und der Kugelfunktionen. Teubner, LeipzigGoogle Scholar
  19. Sternberg S (1969) Celestial mechanics, vol 2. Benjamin, New YorkGoogle Scholar
  20. Synge JL (1960) Relativity: the general theory. North-Holland, AmsterdamMATHGoogle Scholar
  21. Turcotte DL (1997) Fractals and chaos in geology and geophysics, 2nd edn. Cambridge University, CambridgeCrossRefGoogle Scholar

Collections

  1. Anger G, Gorenflo R, Jochmann H, Moritz H, Webers W (1993) Inverse problems: principles and applications in geophysics, technology, and medicine. Mathematical research, vol 74. Akademie Verlag, BerlinGoogle Scholar
  2. Borre K (ed) (2006) Mathematical foundation of geodesy (Selected papers by Torben Krarup). Springer, BerlinMATHGoogle Scholar

Journal Articles

  1. Erker E, Höggerl N, Imrek E, Hofmann-Wellenhof B, Kühtreiber N (2003) The Austrian geoid-recent steps to a new solution. Österreichische Zeitschrift für Vermessung und Geoinformation 91(1):4–13Google Scholar
  2. Hörmander L (1976) The boundary problems of physical geodesy. Arch Ration Mech Anal 62:1–52CrossRefMATHGoogle Scholar
  3. Koch KR (1971) Die geodätische Randwertaufgabe bei bekannter Erdoberfläche. Zeitschrift für Vermessungswesen 96:218–224Google Scholar
  4. Kühtreiber N (2002) High precision geoid determination of Austria using heterogeneous data. In: Tziavos IN (ed) Gravity and geoid 2002. Proceedings of the third meeting of the international gravity and geoid commission, Thessaloniki, Greece, 26–30 Aug 2002. http://olimpia.topo.auth.gr/GG2002/SESSION2/kuehtreiber.pdf or http://olimpia.topo.auth.gr/GG2002/SESSION2/session2.html
  5. Lerch FJ, Klosko SM, Laubscher RE, Wagner CA (1979) Gravity model improvement using Geos 3 (GEM 9 and 10). J Geophys Res 84(B8):3897–3916CrossRefGoogle Scholar
  6. Martinec Z, Grafarend EW (1997) Solution to the Stokes boundary-value problem on an ellipsoid of revolution. Studia Geoph et Geod 41:103–129CrossRefGoogle Scholar
  7. Moritz H (1978) On the convergence of the spherical-harmonic expansion for the geopotential at the Earth’s surface. Bollettino de geodesia e scienze affini 37:363–381Google Scholar
  8. Moritz H (2009) Grosse Mathematiker und die Geowissenschaften: Von Leibniz und Newton bis Einstein and Hilbert, Sitzungsberichte Leibniz-Sozietät der Wissenschaften 104:115–130Google Scholar
  9. Pail R, Kühtreiber N, Wiesenhofer B, Hofmann-Wellenhof B, Of G, Steinbach O, Höggerl N, Imrek E, Ruess D, Ullrich C (2008) Ö.Z. Vermessung und Geoinformation 96(1):3–14Google Scholar
  10. Rummel R, Balmino G, Johannessen J, Visser P, Woodworth P (2002) Dedicated gravity field missions – principles and aims. J Geodynamics 33:3–20CrossRefGoogle Scholar
  11. Stokes GG (1849) On the variation of gravity on the surface of the Earth. Trans Camb Philos Soc 8:672–596Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of NavigationGraz University of TechnologyGrazAustria

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